In his closing vision of the end-times prosperity of the people of God, Zechariah writes,

Then the survivors from all the nations that have attacked Jerusalem will go up year after year to worship the King, Yahweh Almighty, and to celebrate the Feast of Tabernacles. —14:16

What is the significance of their observance of this particular feast? It seems to me that there were more important feasts and celebrations in the Old Testament, such as the Passover, so there must be a special significance to the mention of this particular feast in conjunction with the conversion of the Gentiles. What are your thoughts?

3 Answers
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And it shall be, that whoso of the families of the earth goeth not up unto Jerusalem to worship the King, the LORD of hosts, upon them there shall be no rain.

Sukkot (Tabernacles) is the beginning of the rainy season in the land of Israel. This suggests a direct causal connection: no worship at Sukkot, no rain that winter. No rain, no crops; no crops, no food (and no overflow, see below).

The text continues, reinforcing this theme:

And if the family of Egypt go not up, and come not, they shall have no overflow; there shall be the plague, wherewith the LORD will smite the nations that go not up to keep the feast of tabernacles.
This shall be the punishment of Egypt, and the punishment of all the nations that go not up to keep the feast of tabernacles.

Further, the three festivals -- Pesach, Shavuot, and Sukkot -- are of equal importance; all are pilgrimage festivals for which people were expected to go to Jerusalem (when the temple stood).

Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.

In Zechariah 14:16 the prophet is probably not referring to conversion in the sense of becoming Israelites, (or Jews already at that time). In this passage as in other similar passages the idea is that the nations will recognize the God of Israel as the true God, the only one worthy of worship. Conversion as we think of it today is not required.

The passover holiday is in fact two separate holiday's - the passover sacrifice and the feast of unleavened bread. The passover sacrifice is on the fourteenth of Nisan. The feast of unleavened bread is the following seven days. Participation in the passover sacrifice is limited, first to members of the Israelite community, in Exodus 12:43, and secondly by the requirement to be subscribed to a particular lamb together with a group (Tractate Pessahim 8:7). These requirements make the sacrifice, and indirectly the feast of unleavened bread inappropriate for universal participation.

There are no particular restrictions on participation in the feast of Tabernacles. In terms of sheer joy, it is the ultimate Israelite holiday, often referred to as simply "the holiday". So it is an appropriate time for universal participation.

Nota bene - Passover and Tabernacles are poles apart in the calendar, passover being at the beginning of spring and Tabernacles at the beginning of winter. They are also poles apart in the particular/universal themes of their celebration. In a similar way, the Day of Atonement and Purim are poles apart in calendar and theme. The Day of Atonement being a day of the spirit whereas Purim is definitely a day of the flesh. A similar duality with Weeks and Hanuccah with regard to celebration of the heavenly and earthly Temple service, though this particular duality is not mentioned much now after the row with the Saducees.

The apostle Peter observes that the Old Testament prophets spoke concerning the salvation and grace that are ours in Christ and the glory that is to follow (1 Peter 10-11). In the gospels, Jesus also informs a Samaritan woman (John 4:23) that worship is no longer restricted to any specific geographical location (e.g. Jerusalem and its temple) or to set times and seasons, as was commanded under the Old Covenant dispensation (Deut 16:16). In addition, Paul informs Christians that the Old Testament annual Sabbaths were only shadows of future realities (Col 2:17). From this New Testament perspective, we can see that the prophet's use of this particular Old Testament festival serves to illustrate the in-gathering of the nations that is to take place at the Lord’s return: the Feast of Tabernacles being that great feast of in-gathering which closed the religious year for ancient Israel (Exodus 23:16). This eight day festival was a time of thanksgiving and great rejoicing before the Lord. The tabernacles or booths, themselves, were intended to bring to mind how God had sustained the nation of Israel during the forty years wilderness wondering (Leviticus 23:43) and were also a reminder to them also not to overlook the Lord’s provisions now that they had entered the land of promise being blessed with rain in due season and regular bountiful harvests as a result.

This autumn festival coincided with the latter rain, which brought in the fruit harvest.

Zechariah therefore employs the thought of universal observation of this Old Covenant Festival to picture an end time 'harvest' of souls (Revelation 14:14-16), when “many nations shall be joined to the LORD” and when the Lord himself will tabernacle with his people (Zechariah 2:11; Revelation 21:3). Those who fail to share in this latter 'harvest' are thus presented as falling outside of God's provision (Zechariah 14:18-19).